The interplay between mathematics and theoretical biology has produced an increasingly vibrant research area over the past several years. In using mathematics to test various hypotheses and develop new ones, theoretical biologists have been able to gain insight into myriad biological systems. Despite this progress, the application of mathematics to theoretical biology is still at an early stage.

The Mathematical and Theoretical Biology Institute (MTBI) is an eight-week undergraduate summer research program that has been operating at Cornell University since 1996. With financial support from the National Science Foundation (under the Research Experience for Undergraduates (REU) program), the National Security Agency, the Sloan Foundation, and Cornell, MTBI encourages undergraduates to pursue advanced degrees in mathematics and science and facilitates access to graduate study in the sciences for Latinos, Native Americans, and other underrepresented minorities. Although any student who meets the educational criteria is eligible to participate, MTBI specifically seeks out qualified minority students who are interested in the application of mathematics to the biological sciences. Of the approximately 30 students who participate in MTBI each summer, between two thirds and three quarters are underrepresented minorities.

The experience at MTBI is based on mathematical training and mentoring. The students attend lectures, work in computer laboratories, and, in small groups, conduct research projects. The mathematical focus of the program is dynamical systems (broadly understood to include stochastic processes) and its application to population dynamics, demography, ecology, epidemiology, and evolutionary biology.

The last four weeks of the MTBI program are devoted to student research projects, typically selected by the students themselves. Faculty mentors help provide focus to the projects, but the research is done by the groups of students, applying concepts and techniques learned over the previous few weeks. In the early stages of the projects, the students typically meet with their mentors for 45 minutes each day to discuss their ideas and consider faculty suggestions for possible avenues to pursue. After a few days and (usually) numerous wrong turns, the groups settle on their respective research projects. One or two faculty members are then assigned to each group, meeting with the students on a regular basis to provide guidance and feedback as the projects progress. They also advise the students in the preparation of poster, oral, and written presentations.

Many graduates of the program have gone on to enroll in some of the top applied math, mathematical biology, and statistics programs in the country. A total of 57 MTBI alumni are currently enrolled in graduate school---at Princeton, Harvard, Stanford, Cornell, Oxford University (in England), New York University, the University of Maryland at College Park, and several other institutions.

To give MTBI alumni the opportunity to speak at a national meeting, and to introduce SIAM to MTBI (and vice versa), we organized two minisymposia (Theoretical Biology and Nonlinear Dynamics, Parts I and II) for the 2002 SIAM 50th Anniversary Meeting in Philadelphia. All the speakers presented work of MTBI alumni. Most described projects from their summer research experiences at MTBI. Others reported on work they did while in graduate school, but that was clearly inspired by MTBI.

The projects presented involved applications of mathematics to model biological phenomena or the use of techniques from mathematical epidemiology to study various systems. In a talk titled "A Mathematical Model of a Retinal Oscillator," for example, Erika Camacho (Cornell) described the application of techniques from nonlinear dynamics to model the effects of melatonin on the eyes of developing chicks. (Camacho is on track to become the first MTBI graduate to receive a PhD---from Cornell, in 2003.)

Nicolás Crisosto (University of California, Berkeley) had applied ideas from epidemiology to study the effects of cooperative learning; his talk, "Who Says We R0 Ready for Change," was presented by Stephen Wirkus, one of the supervisors of his project. Brisa Sanchez (Harvard) discussed the use of statistical methods to examine the effect of storage on the detection of prostate cancer in her talk, "Modeling the Detection of Prostate Cancer." The other speakers were Guarionex Jordan-Salivia (University of Iowa), Nandi Leslie (Princeton), Ricardo Saenz (Princeton), and Roberto Saenz (University of Texas, El Paso).

Because the vast majority of MTBI students come from nonselective and/or nonresearch schools, one of the primary goals of MTBI is to make the students aware of the numerous exciting subdisciplines of applied mathematics and, more generally, to open their minds to the wealth of possibilities in both graduate school and careers in science. We hope that interested readers will seek out more information about MTBI, encourage their students to consider applying to this program, and perhaps even help to establish similar programs at other institutions.

Descriptions of all the MTBI student projects have been compiled in a series of Technical Reports, published by the Department of Biological Statistics and Computational Biology (formerly the Department of Biometrics) at Cornell. If you are interested in learning more about MTBI, we encourage you to visit the Web site (www.biom.cornell.edu/MTBI). Information is also available from mtbi@cornell.edu or from MTBI director Carlos Castillo-Chavez, at cc32@cornell.edu.

Stephen Wirkus (swirkus@csupomona.edu) was an MTBI teaching assistant from 1996 to 1998 and has been Summer Director of MTBI since 1999. He is an assistant professor of mathematics at Cal Poly Pomona and an adjunct assistant professor of biological statistics and computational biology at Cornell University.

Mason A. Porter (mason@math.gatech.edu) has been a teaching assistant in the MTBI program for the last three years. In August, he joined the Georgia Tech faculty as a visiting assistant professor in the School of Mathematics and a Research Associate Member of the Center for Nonlinear Science (in the School of Physics).